Piloting a helicopter close to the ground or close to a takeoff area is difficult, in particular if an engine failure occurs during this stage and if the on-board weight is large.
The pilot must manage the air speed of the aircraft, which, during takeoff, is low and rapidly varying, while simultaneously monitoring the speed of rotation of the main rotor and the path followed. It is necessary to gain speed quickly so as to reach as quickly as possible an air speed that makes it possible to begin climbing and thus escape from obstacles and geographical relief around the takeoff area.
A takeoff is generally performed as follows:                the helicopter rises a little, to a small height vertically above its takeoff point, with the pilot then accelerating so that the speed of the helicopter reaches a threshold value TOSS (takeoff safety speed); and        once the helicopter has reached the speed TOSS, it can begin to climb, with said speed TOSS guaranteeing a minimum climb rate of 100 feet per minute (ft/min) on a single engine and enabling the helicopter, even in the event of an engine failure, to overfly a standardized obstacle and continue climbing.        
It should be observed that the takeoff safety speed depends essentially on the weight of the aircraft and on atmospheric conditions (pressure and temperature).
Several observations encourage research and development of means for providing assistance in piloting (or indeed automatic piloting) during takeoff:                piloting is genuinely difficult and on a twin-engine aircraft having modest single-engine performance, the failure of one of the engines during takeoff can become critical;        the configuration of a takeoff platform is not always compatible with complying with optimum procedures as defined for takeoff: for example it may not be possible to reverse on the platform;        only a procedure based solely on maneuvers going forwards and upwards can be compatible with all environments; and        a procedure that is automatic and integrated in an autopilot makes it easier to obtain certification, since the reproducibility and the safety of the procedure are then guaranteed.        
Unless stated to the contrary, in the meaning of the present application, the term “twin-engine” covers “multi-engine” and the term “single-engine” covers “multi-engine having at least one engine that is inoperative”.
Certain autopilots include a mode enabling a radio altimeter setpoint altitude to be captured and held, as well as enabling a predefined vertical speed to be captured and held; during takeoff, after a decision height has been passed, the autopilot can apply an order to the cyclic pitch control so as to achieve a nose-down attitude of −8°, for example, and then allow speed to increase until the indicated air speed (IAS) reaches a valid value, i.e. a speed close to at least 15 meters per second (m/s); engaging this mode then makes it possible to accelerate until an optimum climb speed (OCS) (frequently written Vy) is reached, which speed may be close to 35 m/s to 40 m/s, with acceleration being about 0.7 meters per second per second (m/s2).
That procedure presents drawbacks:                acceleration at that level may be satisfactory in twin-engine operation, but it is insufficient in single-engine operation (after a failure);        piloting the attitude of the aircraft does not allow full advantage to be taken of helicopter performance on takeoff, where said performance is associated directly with the power available, which power varies depending on whether the helicopter is in single-engine operation or in twin-engine operation.        
Thus, the use of that mode does not enable single-engine flight to be optimized.
Furthermore, so far as the inventor is aware, there are no systems in existence that enable the value of TOSS to be adjusted, nor any that manage the power of a twin-engine helicopter optimally while flying on a single engine.
Various systems have been proposed for providing assistance in piloting an aircraft during takeoff and/or landing.
U.S. Pat. No. 3,407,654 describes an instrument for piloting on takeoff that implements a first stage of maximum pitch attitude followed by a second stage of maximum acceleration.
U.S. Pat. No. 3,916,688 and FR 2 174 070 describe apparatus for controlling the flight of a vehicle during vertical or short takeoff and landing along a glide path, using a program of constant or variable deceleration.
U.S. Pat. No. 3,945,590 and FR 2 298 822 describe a system for controlling takeoff that is semiautomatic after a run on the ground, and that limits the amplitude or the pitch attitude the pilot can command, and that enables the desired altitude to be reached asymptotically.
U.S. Pat. No. 3,927,306 and FR 2 274 971 relate to apparatus for controlling the flight path of an aircraft, for following a rectilinear path with programmed acceleration along the path until the desired speed is reached.
U.S. Pat. No. 6,527,225 describes a method of automating takeoff of a multi-engine helicopter along a takeoff path that includes a decision point; the flight controls are controlled as a function of differences between the path and the actual position of the helicopter as given by a positioning system (GPS); in the event of an engine failure being detected before the decision point is reached, the automatic pilot controls the cyclic pitch and the collective pitch to cause the aircraft to land; in the event of such a failure being detected after the decision point has been passed, the automatic pilot monitors the speed of the rotor and adjusts the collective pitch to cause the helicopter to follow a different takeoff path.